Pith Number

pith:KGJN7DKM

pith:2012:KGJN7DKM464XEDK6JKXSJPSQQ5

not attested not anchored not stored refs pending

An upper bound for the crossing number of augmented cubes

Guoqing Wang, Haoli Wang, Wenping Zheng, Xuezhi Yang, Yuansheng Yang

arxiv:1210.6161 v1 · 2012-10-23 · math.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{KGJN7DKM464XEDK6JKXSJPSQQ5}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T03:42:33.030424Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

5192df8d4ce7b9720d5e4aaf24be508763452af287a99a477421f36f82642321

Aliases

arxiv: 1210.6161 · arxiv_version: 1210.6161v1 · doi: 10.48550/arxiv.1210.6161 · pith_short_12: KGJN7DKM464X · pith_short_16: KGJN7DKM464XEDK6 · pith_short_8: KGJN7DKM

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/KGJN7DKM464XEDK6JKXSJPSQQ5 \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 5192df8d4ce7b9720d5e4aaf24be508763452af287a99a477421f36f82642321

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "2f7b6b5f7bab0fd5b5f1b6aa6d453aaf1c890bb235fdb33f775cc614e10ccfc2",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "math.CO",
    "submitted_at": "2012-10-23T08:16:11Z",
    "title_canon_sha256": "13c5f5ee62342b76bc67bf05964a92435852689f774e23b4f6a6789b660a3616"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1210.6161",
    "kind": "arxiv",
    "version": 1
  }
}